Small Vibratory Motions of Elastic Fluids. 289 



and the wave will forsake the tliaphragm. Tiie motion will thence- 

 forth be indicated by the uniform propagation of the curve y'e'w'd', 

 of which the portions /'e' and e'li'd', are exactly ecpial to fe and 

 end. Or it may be indicated by the disjointed portions /,e^, m,n,, 

 c,d^, which possess the advantage of shewing the etfect of sud- 

 denly stopping the diaphragm. As the motion represented by 

 Xe, is just equal and opposite to that represented by m,n,, one 

 destroys the other. Hence the motion of translation of each 

 particle, is that which it would receive by going through the 

 velocities represented by the curve c,d,, and is therefore just equal 

 to that of the diaphragm ; as it plainly ought to be. 



T^e may gather from what precedes, that a particle may go 

 through velocities represented by a portion of the primary curve, 

 such as n^d„ only one extremity of which is situated in the axis : 

 and it matters not what is the subsequent motion, because the 

 movement is equally possible if a loop pqr, terminated at one 

 end in r, the foot of the ordinate to n, be superadded to the line 

 f'e'n'd', and the motion be such as will be given by a line traced 

 by taking- ordinates equal to the sum of the corresponding 

 oidinates of these two lines. As the dimensions of the loop are 

 arbitrary, the resulting line is also arbitrary. We may now shew 

 that a particle may perform the motion indicated by any 

 portion whatever of the primary curve, the prior and sub- 

 .sequent motions being arbitrary. And first it is obvious, that 

 as the particles are susceptible of the motion which results 

 from the proj)agation of the curve /end, (Fig. 4.) in the direc- 

 tion fd, they are equally susceptible of that which results from 

 a propagation of the same curve in the contrary direction. 

 For at any given instant, the condensations are the same and 

 in the same order in the two cases, and, consequently, the 

 particles have the same relative positions. Therefore if these 

 positions be possible in one case, they must be so in the other. 



Vol. in. Part I. Oo 



